LMFDB - Embedded newform 1849.4.a.j.1.49

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$109.094531601$
Analytic rank:	$1$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.49
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.40604 q^{2} +2.51556 q^{3} +21.2252 q^{4} +3.24888 q^{5} +13.5992 q^{6} -35.6131 q^{7} +71.4960 q^{8} -20.6720 q^{9} +O(q^{10})$	\(q+5.40604 q^{2} +2.51556 q^{3} +21.2252 q^{4} +3.24888 q^{5} +13.5992 q^{6} -35.6131 q^{7} +71.4960 q^{8} -20.6720 q^{9} +17.5635 q^{10} -42.5559 q^{11} +53.3932 q^{12} +22.6295 q^{13} -192.525 q^{14} +8.17273 q^{15} +216.708 q^{16} -6.66526 q^{17} -111.753 q^{18} -14.7438 q^{19} +68.9581 q^{20} -89.5866 q^{21} -230.059 q^{22} -95.0580 q^{23} +179.852 q^{24} -114.445 q^{25} +122.336 q^{26} -119.922 q^{27} -755.895 q^{28} -125.391 q^{29} +44.1820 q^{30} +56.0788 q^{31} +599.564 q^{32} -107.052 q^{33} -36.0326 q^{34} -115.702 q^{35} -438.767 q^{36} -217.165 q^{37} -79.7056 q^{38} +56.9257 q^{39} +232.282 q^{40} +342.891 q^{41} -484.308 q^{42} -903.258 q^{44} -67.1607 q^{45} -513.887 q^{46} -399.043 q^{47} +545.141 q^{48} +925.290 q^{49} -618.693 q^{50} -16.7668 q^{51} +480.316 q^{52} +211.948 q^{53} -648.300 q^{54} -138.259 q^{55} -2546.19 q^{56} -37.0889 q^{57} -677.869 q^{58} -435.319 q^{59} +173.468 q^{60} +693.529 q^{61} +303.164 q^{62} +736.193 q^{63} +1507.60 q^{64} +73.5204 q^{65} -578.725 q^{66} -141.684 q^{67} -141.472 q^{68} -239.124 q^{69} -625.491 q^{70} -632.678 q^{71} -1477.96 q^{72} +736.909 q^{73} -1174.00 q^{74} -287.892 q^{75} -312.941 q^{76} +1515.55 q^{77} +307.743 q^{78} +165.173 q^{79} +704.058 q^{80} +256.474 q^{81} +1853.68 q^{82} -1207.11 q^{83} -1901.50 q^{84} -21.6546 q^{85} -315.428 q^{87} -3042.58 q^{88} -385.206 q^{89} -363.073 q^{90} -805.906 q^{91} -2017.63 q^{92} +141.069 q^{93} -2157.24 q^{94} -47.9008 q^{95} +1508.24 q^{96} +625.326 q^{97} +5002.15 q^{98} +879.715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 10 q^{2} + 2 q^{3} + 186 q^{4} - 8 q^{5} - 51 q^{6} + 6 q^{7} + 138 q^{8} + 360 q^{9}+O(q^{10}) $ 50 * q + 10 * q^2 + 2 * q^3 + 186 * q^4 - 8 * q^5 - 51 * q^6 + 6 * q^7 + 138 * q^8 + 360 * q^9	\( 50 q + 10 q^{2} + 2 q^{3} + 186 q^{4} - 8 q^{5} - 51 q^{6} + 6 q^{7} + 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} + 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} + 386 q^{18} - 12 q^{19} - 108 q^{20} - 408 q^{21} - 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} - 1493 q^{26} - 10 q^{27} + 242 q^{28} - 208 q^{29} + 48 q^{30} - 932 q^{31} + 1124 q^{32} - 254 q^{33} - 765 q^{34} - 1452 q^{35} + 747 q^{36} + 90 q^{37} - 1213 q^{38} + 1610 q^{39} - 1693 q^{40} - 1354 q^{41} + 16 q^{42} - 2704 q^{44} - 4508 q^{45} - 233 q^{46} - 3484 q^{47} + 376 q^{48} + 1324 q^{49} + 408 q^{50} - 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} + 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} - 1172 q^{61} + 1546 q^{62} + 3686 q^{63} + 606 q^{64} - 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} - 136 q^{69} + 1310 q^{70} - 162 q^{71} + 5814 q^{72} - 746 q^{73} - 4332 q^{74} - 236 q^{75} - 1338 q^{76} - 2024 q^{77} - 2782 q^{78} - 2656 q^{79} + 5713 q^{80} - 86 q^{81} + 4168 q^{82} - 3514 q^{83} - 4269 q^{84} + 7558 q^{85} - 10278 q^{87} - 11692 q^{88} - 2640 q^{89} - 8286 q^{90} + 5946 q^{91} - 4271 q^{92} + 2 q^{93} - 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} + 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q + 10 * q^2 + 2 * q^3 + 186 * q^4 - 8 * q^5 - 51 * q^6 + 6 * q^7 + 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 + 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 + 386 * q^18 - 12 * q^19 - 108 * q^20 - 408 * q^21 - 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 - 1493 * q^26 - 10 * q^27 + 242 * q^28 - 208 * q^29 + 48 * q^30 - 932 * q^31 + 1124 * q^32 - 254 * q^33 - 765 * q^34 - 1452 * q^35 + 747 * q^36 + 90 * q^37 - 1213 * q^38 + 1610 * q^39 - 1693 * q^40 - 1354 * q^41 + 16 * q^42 - 2704 * q^44 - 4508 * q^45 - 233 * q^46 - 3484 * q^47 + 376 * q^48 + 1324 * q^49 + 408 * q^50 - 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 + 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 - 1172 * q^61 + 1546 * q^62 + 3686 * q^63 + 606 * q^64 - 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 - 136 * q^69 + 1310 * q^70 - 162 * q^71 + 5814 * q^72 - 746 * q^73 - 4332 * q^74 - 236 * q^75 - 1338 * q^76 - 2024 * q^77 - 2782 * q^78 - 2656 * q^79 + 5713 * q^80 - 86 * q^81 + 4168 * q^82 - 3514 * q^83 - 4269 * q^84 + 7558 * q^85 - 10278 * q^87 - 11692 * q^88 - 2640 * q^89 - 8286 * q^90 + 5946 * q^91 - 4271 * q^92 + 2 * q^93 - 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 + 2826 * q^98 - 8174 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	5.40604	1.91132	0.955661	−	0.294469i	$-0.0951428\pi$
$2$	5.40604	1.91132	0.955661	+	0.294469i	$0.0951428\pi$
$3$	2.51556	0.484119	0.242059	−	0.970261i	$-0.422177\pi$
$3$	2.51556	0.484119	0.242059	+	0.970261i	$0.422177\pi$
$4$	21.2252	2.65315
$5$	3.24888	0.290588	0.145294	−	0.989389i	$-0.453587\pi$
$5$	3.24888	0.290588	0.145294	+	0.989389i	$0.453587\pi$
$6$	13.5992	0.925307
$7$	−35.6131	−1.92292	−0.961462	−	0.274937i	$-0.911343\pi$
$7$	−35.6131	−1.92292	−0.961462	+	0.274937i	$0.911343\pi$
$8$	71.4960	3.15971
$9$	−20.6720	−0.765629
$10$	17.5635	0.555408
$11$	−42.5559	−1.16646	−0.583231	−	0.812306i	$-0.698212\pi$
$11$	−42.5559	−1.16646	−0.583231	+	0.812306i	$0.698212\pi$
$12$	53.3932	1.28444
$13$	22.6295	0.482792	0.241396	−	0.970427i	$-0.422395\pi$
$13$	22.6295	0.482792	0.241396	+	0.970427i	$0.422395\pi$
$14$	−192.525	−3.67533
$15$	8.17273	0.140679
$16$	216.708	3.38606
$17$	−6.66526	−0.0950919	−0.0475460	−	0.998869i	$-0.515140\pi$
$17$	−6.66526	−0.0950919	−0.0475460	+	0.998869i	$0.515140\pi$
$18$	−111.753	−1.46336
$19$	−14.7438	−0.178024	−0.0890122	−	0.996031i	$-0.528371\pi$
$19$	−14.7438	−0.178024	−0.0890122	+	0.996031i	$0.528371\pi$
$20$	68.9581	0.770975
$21$	−89.5866	−0.930924
$22$	−230.059	−2.22948
$23$	−95.0580	−0.861781	−0.430891	−	0.902404i	$-0.641801\pi$
$23$	−95.0580	−0.861781	−0.430891	+	0.902404i	$0.641801\pi$
$24$	179.852	1.52967
$25$	−114.445	−0.915558
$26$	122.336	0.922771
$27$	−119.922	−0.854774
$28$	−755.895	−5.10181
$29$	−125.391	−0.802915	−0.401458	−	0.915878i	$-0.631496\pi$
$29$	−125.391	−0.802915	−0.401458	+	0.915878i	$0.631496\pi$
$30$	44.1820	0.268883
$31$	56.0788	0.324905	0.162452	−	0.986716i	$-0.448060\pi$
$31$	56.0788	0.324905	0.162452	+	0.986716i	$0.448060\pi$
$32$	599.564	3.31215
$33$	−107.052	−0.564706
$34$	−36.0326	−0.181751
$35$	−115.702	−0.558779
$36$	−438.767	−2.03133
$37$	−217.165	−0.964911	−0.482456	−	0.875920i	$-0.660255\pi$
$37$	−217.165	−0.964911	−0.482456	+	0.875920i	$0.660255\pi$
$38$	−79.7056	−0.340262
$39$	56.9257	0.233729
$40$	232.282	0.918174
$41$	342.891	1.30611	0.653055	−	0.757310i	$-0.273487\pi$
$41$	342.891	1.30611	0.653055	+	0.757310i	$0.273487\pi$
$42$	−484.308	−1.77930
$43$	0	0
$43$	0	0
$44$	−903.258	−3.09480
$45$	−67.1607	−0.222483
$46$	−513.887	−1.64714
$47$	−399.043	−1.23843	−0.619217	−	0.785220i	$-0.712550\pi$
$47$	−399.043	−1.23843	−0.619217	+	0.785220i	$0.712550\pi$
$48$	545.141	1.63926
$49$	925.290	2.69764
$50$	−618.693	−1.74993
$51$	−16.7668	−0.0460358
$52$	480.316	1.28092
$53$	211.948	0.549307	0.274653	−	0.961543i	$-0.411437\pi$
$53$	211.948	0.549307	0.274653	+	0.961543i	$0.411437\pi$
$54$	−648.300	−1.63375
$55$	−138.259	−0.338960
$56$	−2546.19	−6.07588
$57$	−37.0889	−0.0861850
$58$	−677.869	−1.53463
$59$	−435.319	−0.960572	−0.480286	−	0.877112i	$-0.659467\pi$
$59$	−435.319	−0.960572	−0.480286	+	0.877112i	$0.659467\pi$
$60$	173.468	0.373243
$61$	693.529	1.45569	0.727847	−	0.685740i	$-0.240521\pi$
$61$	693.529	1.45569	0.727847	+	0.685740i	$0.240521\pi$
$62$	303.164	0.620998
$63$	736.193	1.47225
$64$	1507.60	2.94453
$65$	73.5204	0.140294
$66$	−578.725	−1.07934
$67$	−141.684	−0.258351	−0.129175	−	0.991622i	$-0.541233\pi$
$67$	−141.684	−0.258351	−0.129175	+	0.991622i	$0.541233\pi$
$68$	−141.472	−0.252293
$69$	−239.124	−0.417205
$70$	−625.491	−1.06801
$71$	−632.678	−1.05754	−0.528768	−	0.848766i	$-0.677346\pi$
$71$	−632.678	−1.05754	−0.528768	+	0.848766i	$0.677346\pi$
$72$	−1477.96	−2.41916
$73$	736.909	1.18149	0.590744	−	0.806859i	$-0.298834\pi$
$73$	736.909	1.18149	0.590744	+	0.806859i	$0.298834\pi$
$74$	−1174.00	−1.84426
$75$	−287.892	−0.443239
$76$	−312.941	−0.472326
$77$	1515.55	2.24302
$78$	307.743	0.446731
$79$	165.173	0.235233	0.117617	−	0.993059i	$-0.462475\pi$
$79$	165.173	0.235233	0.117617	+	0.993059i	$0.462475\pi$
$80$	704.058	0.983951
$81$	256.474	0.351817
$82$	1853.68	2.49640
$83$	−1207.11	−1.59635	−0.798177	−	0.602422i	$-0.794202\pi$
$83$	−1207.11	−1.59635	−0.798177	+	0.602422i	$0.794202\pi$
$84$	−1901.50	−2.46988
$85$	−21.6546	−0.0276326
$86$	0	0
$87$	−315.428	−0.388706
$88$	−3042.58	−3.68568
$89$	−385.206	−0.458783	−0.229392	−	0.973334i	$-0.573674\pi$
$89$	−385.206	−0.458783	−0.229392	+	0.973334i	$0.573674\pi$
$90$	−363.073	−0.425236
$91$	−805.906	−0.928372
$92$	−2017.63	−2.28644
$93$	141.069	0.157293
$94$	−2157.24	−2.36705
$95$	−47.9008	−0.0517318
$96$	1508.24	1.60348
$97$	625.326	0.654559	0.327279	−	0.944928i	$-0.393868\pi$
$97$	625.326	0.654559	0.327279	+	0.944928i	$0.393868\pi$
$98$	5002.15	5.15606
$99$	879.715	0.893077
$100$	−2429.12	−2.42912
$101$	−112.459	−0.110793	−0.0553965	−	0.998464i	$-0.517642\pi$
$101$	−112.459	−0.110793	−0.0553965	+	0.998464i	$0.517642\pi$
$102$	−90.6421	−0.0879892
$103$	−1643.53	−1.57225	−0.786124	−	0.618068i	$-0.787916\pi$
$103$	−1643.53	−1.57225	−0.786124	+	0.618068i	$0.787916\pi$
$104$	1617.92	1.52548
$105$	−291.056	−0.270516
$106$	1145.80	1.04990
$107$	865.531	0.782001	0.391000	−	0.920391i	$-0.372129\pi$
$107$	865.531	0.782001	0.391000	+	0.920391i	$0.372129\pi$
$108$	−2545.36	−2.26785
$109$	147.602	0.129703	0.0648517	−	0.997895i	$-0.479343\pi$
$109$	147.602	0.129703	0.0648517	+	0.997895i	$0.479343\pi$
$110$	−747.432	−0.647862
$111$	−546.291	−0.467132
$112$	−7717.64	−6.51115
$113$	−1485.11	−1.23635	−0.618176	−	0.786040i	$-0.712128\pi$
$113$	−1485.11	−1.23635	−0.618176	+	0.786040i	$0.712128\pi$
$114$	−200.504	−0.164727
$115$	−308.832	−0.250424
$116$	−2661.45	−2.13026
$117$	−467.797	−0.369639
$118$	−2353.35	−1.83596
$119$	237.370	0.182855
$120$	584.317	0.444505
$121$	480.004	0.360634
$122$	3749.24	2.78230
$123$	862.561	0.632313
$124$	1190.28	0.862022
$125$	−777.926	−0.556639
$126$	3979.88	2.81394
$127$	−24.8952	−0.0173944	−0.00869721	−	0.999962i	$-0.502768\pi$
$127$	−24.8952	−0.0173944	−0.00869721	+	0.999962i	$0.502768\pi$
$128$	3353.62	2.31579
$129$	0	0
$130$	397.454	0.268146
$131$	1737.49	1.15882	0.579409	−	0.815037i	$-0.303284\pi$
$131$	1737.49	1.15882	0.579409	+	0.815037i	$0.303284\pi$
$132$	−2272.20	−1.49825
$133$	525.073	0.342328
$134$	−765.950	−0.493791
$135$	−389.610	−0.248387
$136$	−476.539	−0.300463
$137$	547.378	0.341355	0.170678	−	0.985327i	$-0.445404\pi$
$137$	547.378	0.341355	0.170678	+	0.985327i	$0.445404\pi$
$138$	−1292.71	−0.797412
$139$	2059.83	1.25692	0.628462	−	0.777840i	$-0.283685\pi$
$139$	2059.83	1.25692	0.628462	+	0.777840i	$0.283685\pi$
$140$	−2455.81	−1.48253
$141$	−1003.82	−0.599550
$142$	−3420.28	−2.02129
$143$	−963.018	−0.563158
$144$	−4479.79	−2.59247
$145$	−407.380	−0.233318
$146$	3983.75	2.25820
$147$	2327.62	1.30598
$148$	−4609.38	−2.56006
$149$	−581.330	−0.319627	−0.159814	−	0.987147i	$-0.551089\pi$
$149$	−581.330	−0.319627	−0.159814	+	0.987147i	$0.551089\pi$
$150$	−1556.36	−0.847173
$151$	291.912	0.157321	0.0786604	−	0.996901i	$-0.474936\pi$
$151$	291.912	0.157321	0.0786604	+	0.996901i	$0.474936\pi$
$152$	−1054.12	−0.562505
$153$	137.784	0.0728051
$154$	8193.09	4.28713
$155$	182.193	0.0944135
$156$	1208.26	0.620117
$157$	1119.70	0.569181	0.284591	−	0.958649i	$-0.408142\pi$
$157$	1119.70	0.569181	0.284591	+	0.958649i	$0.408142\pi$
$158$	892.932	0.449607
$159$	533.166	0.265930
$160$	1947.91	0.962473
$161$	3385.31	1.65714
$162$	1386.51	0.672435
$163$	−1952.25	−0.938111	−0.469055	−	0.883169i	$-0.655406\pi$
$163$	−1952.25	−0.938111	−0.469055	+	0.883169i	$0.655406\pi$
$164$	7277.93	3.46531
$165$	−347.798	−0.164097
$166$	−6525.68	−3.05115
$167$	2143.75	0.993342	0.496671	−	0.867939i	$-0.334555\pi$
$167$	2143.75	0.993342	0.496671	+	0.867939i	$0.334555\pi$
$168$	−6405.08	−2.94145
$169$	−1684.91	−0.766912
$170$	−117.066	−0.0528148
$171$	304.784	0.136301
$172$	0	0
$173$	−414.204	−0.182031	−0.0910154	−	0.995849i	$-0.529011\pi$
$173$	−414.204	−0.182031	−0.0910154	+	0.995849i	$0.529011\pi$
$174$	−1705.22	−0.742943
$175$	4075.73	1.76055
$176$	−9222.21	−3.94972
$177$	−1095.07	−0.465031
$178$	−2082.44	−0.876883
$179$	399.199	0.166690	0.0833450	−	0.996521i	$-0.473440\pi$
$179$	399.199	0.166690	0.0833450	+	0.996521i	$0.473440\pi$
$180$	−1425.50	−0.590281
$181$	848.060	0.348264	0.174132	−	0.984722i	$-0.444288\pi$
$181$	848.060	0.348264	0.174132	+	0.984722i	$0.444288\pi$
$182$	−4356.75	−1.77442
$183$	1744.61	0.704729
$184$	−6796.27	−2.72298
$185$	−705.542	−0.280392
$186$	762.626	0.300637
$187$	283.646	0.110921
$188$	−8469.78	−3.28576
$189$	4270.77	1.64367
$190$	−258.954	−0.0988762
$191$	−2352.82	−0.891332	−0.445666	−	0.895199i	$-0.647033\pi$
$191$	−2352.82	−0.891332	−0.445666	+	0.895199i	$0.647033\pi$
$192$	3792.45	1.42550
$193$	4800.09	1.79025	0.895125	−	0.445816i	$-0.147086\pi$
$193$	4800.09	1.79025	0.895125	+	0.445816i	$0.147086\pi$
$194$	3380.53	1.25107
$195$	184.945	0.0679188
$196$	19639.5	7.15725
$197$	−1982.45	−0.716974	−0.358487	−	0.933535i	$-0.616707\pi$
$197$	−1982.45	−0.716974	−0.358487	+	0.933535i	$0.616707\pi$
$198$	4755.77	1.70696
$199$	2500.62	0.890774	0.445387	−	0.895338i	$-0.353066\pi$
$199$	2500.62	0.890774	0.445387	+	0.895338i	$0.353066\pi$
$200$	−8182.34	−2.89290
$201$	−356.415	−0.125072
$202$	−607.957	−0.211761
$203$	4465.56	1.54395
$204$	−355.880	−0.122140
$205$	1114.01	0.379540
$206$	−8884.97	−3.00507
$207$	1965.04	0.659805
$208$	4904.00	1.63476
$209$	627.436	0.207659
$210$	−1573.46	−0.517042
$211$	−5317.49	−1.73493	−0.867466	−	0.497496i	$-0.834253\pi$
$211$	−5317.49	−1.73493	−0.867466	+	0.497496i	$0.834253\pi$
$212$	4498.64	1.45739
$213$	−1591.54	−0.511973
$214$	4679.09	1.49466
$215$	0	0
$216$	−8573.91	−2.70084
$217$	−1997.14	−0.624767
$218$	797.940	0.247905
$219$	1853.73	0.571981
$220$	−2934.57	−0.899313
$221$	−150.831	−0.0459096
$222$	−2953.27	−0.892839
$223$	6017.56	1.80702	0.903511	−	0.428566i	$-0.140981\pi$
$223$	6017.56	1.80702	0.903511	+	0.428566i	$0.140981\pi$
$224$	−21352.3	−6.36902
$225$	2365.80	0.700978
$226$	−8028.58	−2.36307
$227$	1324.60	0.387298	0.193649	−	0.981071i	$-0.437968\pi$
$227$	1324.60	0.387298	0.193649	+	0.981071i	$0.437968\pi$
$228$	−787.220	−0.228662
$229$	−2621.79	−0.756561	−0.378281	−	0.925691i	$-0.623485\pi$
$229$	−2621.79	−0.756561	−0.378281	+	0.925691i	$0.623485\pi$
$230$	−1669.56	−0.478640
$231$	3812.44	1.08589
$232$	−8964.96	−2.53698
$233$	−5136.07	−1.44410	−0.722050	−	0.691841i	$-0.756800\pi$
$233$	−5136.07	−1.44410	−0.722050	+	0.691841i	$0.756800\pi$
$234$	−2528.92	−0.706500
$235$	−1296.44	−0.359875
$236$	−9239.75	−2.54854
$237$	415.502	0.113881
$238$	1283.23	0.349494
$239$	−3084.80	−0.834893	−0.417446	−	0.908702i	$-0.637075\pi$
$239$	−3084.80	−0.834893	−0.417446	+	0.908702i	$0.637075\pi$
$240$	1771.10	0.476349
$241$	2349.42	0.627966	0.313983	−	0.949429i	$-0.398337\pi$
$241$	2349.42	0.627966	0.313983	+	0.949429i	$0.398337\pi$
$242$	2594.92	0.689288
$243$	3883.06	1.02510
$244$	14720.3	3.86218
$245$	3006.15	0.783902
$246$	4663.03	1.20855
$247$	−333.645	−0.0859487
$248$	4009.41	1.02660
$249$	−3036.55	−0.772825
$250$	−4205.50	−1.06392
$251$	−2635.49	−0.662751	−0.331376	−	0.943499i	$-0.607513\pi$
$251$	−2635.49	−0.662751	−0.331376	+	0.943499i	$0.607513\pi$
$252$	15625.8	3.90609
$253$	4045.28	1.00524
$254$	−134.584	−0.0332463
$255$	−54.4734	−0.0133775
$256$	6068.99	1.48169
$257$	2469.84	0.599472	0.299736	−	0.954022i	$-0.403101\pi$
$257$	2469.84	0.599472	0.299736	+	0.954022i	$0.403101\pi$
$258$	0	0
$259$	7733.91	1.85545
$260$	1560.49	0.372220
$261$	2592.08	0.614735
$262$	9392.93	2.21487
$263$	−1293.67	−0.303313	−0.151656	−	0.988433i	$-0.548461\pi$
$263$	−1293.67	−0.303313	−0.151656	+	0.988433i	$0.548461\pi$
$264$	−7653.77	−1.78431
$265$	688.592	0.159622
$266$	2838.56	0.654298
$267$	−969.006	−0.222106
$268$	−3007.28	−0.685443
$269$	−3344.50	−0.758060	−0.379030	−	0.925384i	$-0.623742\pi$
$269$	−3344.50	−0.758060	−0.379030	+	0.925384i	$0.623742\pi$
$270$	−2106.25	−0.474748
$271$	1532.27	0.343465	0.171732	−	0.985144i	$-0.445064\pi$
$271$	1532.27	0.343465	0.171732	+	0.985144i	$0.445064\pi$
$272$	−1444.42	−0.321987
$273$	−2027.30	−0.449442
$274$	2959.15	0.652440
$275$	4870.30	1.06796
$276$	−5075.45	−1.10691
$277$	6489.77	1.40770	0.703849	−	0.710350i	$-0.251463\pi$
$277$	6489.77	1.40770	0.703849	+	0.710350i	$0.251463\pi$
$278$	11135.5	2.40239
$279$	−1159.26	−0.248757
$280$	−8272.26	−1.76558
$281$	−2862.27	−0.607648	−0.303824	−	0.952728i	$-0.598263\pi$
$281$	−2862.27	−0.607648	−0.303824	+	0.952728i	$0.598263\pi$
$282$	−5426.66	−1.14593
$283$	5939.25	1.24753	0.623767	−	0.781611i	$-0.285602\pi$
$283$	5939.25	1.24753	0.623767	+	0.781611i	$0.285602\pi$
$284$	−13428.7	−2.80580
$285$	−120.497	−0.0250443
$286$	−5206.11	−1.07638
$287$	−12211.4	−2.51155
$288$	−12394.2	−2.53588
$289$	−4868.57	−0.990958
$290$	−2202.31	−0.445945
$291$	1573.04	0.316884
$292$	15641.0	3.13467
$293$	7464.27	1.48828	0.744142	−	0.668022i	$-0.232859\pi$
$293$	7464.27	1.48828	0.744142	+	0.668022i	$0.232859\pi$
$294$	12583.2	2.49614
$295$	−1414.30	−0.279131
$296$	−15526.4	−3.04884
$297$	5103.37	0.997062
$298$	−3142.69	−0.610910
$299$	−2151.12	−0.416061
$300$	−6110.57	−1.17598
$301$	0	0
$302$	1578.08	0.300691
$303$	−282.897	−0.0536370
$304$	−3195.11	−0.602802
$305$	2253.19	0.423007
$306$	744.866	0.139154
$307$	−1428.88	−0.265637	−0.132818	−	0.991140i	$-0.542403\pi$
$307$	−1428.88	−0.265637	−0.132818	+	0.991140i	$0.542403\pi$
$308$	32167.8	5.95107
$309$	−4134.39	−0.761155
$310$	984.942	0.180455
$311$	−6168.29	−1.12467	−0.562334	−	0.826910i	$-0.690096\pi$
$311$	−6168.29	−1.12467	−0.562334	+	0.826910i	$0.690096\pi$
$312$	4069.96	0.738514
$313$	−208.901	−0.0377245	−0.0188623	−	0.999822i	$-0.506004\pi$
$313$	−208.901	−0.0377245	−0.0188623	+	0.999822i	$0.506004\pi$
$314$	6053.11	1.08789
$315$	2391.80	0.427818
$316$	3505.84	0.624110
$317$	−392.532	−0.0695483	−0.0347741	−	0.999395i	$-0.511071\pi$
$317$	−392.532	−0.0695483	−0.0347741	+	0.999395i	$0.511071\pi$
$318$	2882.32	0.508277
$319$	5336.13	0.936570
$320$	4898.00	0.855645
$321$	2177.29	0.378581
$322$	18301.1	3.16733
$323$	98.2714	0.0169287
$324$	5443.72	0.933423
$325$	−2589.83	−0.442024
$326$	−10553.9	−1.79303
$327$	371.300	0.0627919
$328$	24515.3	4.12693
$329$	14211.2	2.38142
$330$	−1880.21	−0.313642
$331$	−1850.13	−0.307228	−0.153614	−	0.988131i	$-0.549091\pi$
$331$	−1850.13	−0.307228	−0.153614	+	0.988131i	$0.549091\pi$
$332$	−25621.2	−4.23537
$333$	4489.23	0.738764
$334$	11589.2	1.89860
$335$	−460.315	−0.0750736
$336$	−19414.1	−3.15217
$337$	−2895.95	−0.468109	−0.234054	−	0.972224i	$-0.575199\pi$
$337$	−2895.95	−0.468109	−0.234054	+	0.972224i	$0.575199\pi$
$338$	−9108.66	−1.46582
$339$	−3735.89	−0.598541
$340$	−459.624	−0.0733135
$341$	−2386.48	−0.378989
$342$	1647.67	0.260514
$343$	−20737.1	−3.26443
$344$	0	0
$345$	−776.883	−0.121235
$346$	−2239.20	−0.347919
$347$	−9809.84	−1.51764	−0.758818	−	0.651303i	$-0.774223\pi$
$347$	−9809.84	−1.51764	−0.758818	+	0.651303i	$0.774223\pi$
$348$	−6695.03	−1.03130
$349$	−3828.19	−0.587158	−0.293579	−	0.955935i	$-0.594846\pi$
$349$	−3828.19	−0.587158	−0.293579	+	0.955935i	$0.594846\pi$
$350$	22033.5	3.36498
$351$	−2713.76	−0.412678
$352$	−25515.0	−3.86350
$353$	7778.32	1.17280	0.586399	−	0.810022i	$-0.300545\pi$
$353$	7778.32	1.17280	0.586399	+	0.810022i	$0.300545\pi$
$354$	−5919.99	−0.888824
$355$	−2055.49	−0.307307
$356$	−8176.07	−1.21722
$357$	597.118	0.0885234
$358$	2158.08	0.318598
$359$	2684.71	0.394689	0.197345	−	0.980334i	$-0.436768\pi$
$359$	2684.71	0.394689	0.197345	+	0.980334i	$0.436768\pi$
$360$	−4801.72	−0.702980
$361$	−6641.62	−0.968307
$362$	4584.64	0.665645
$363$	1207.48	0.174590
$364$	−17105.5	−2.46311
$365$	2394.12	0.343327
$366$	9431.43	1.34696
$367$	−10736.5	−1.52709	−0.763545	−	0.645754i	$-0.776543\pi$
$367$	−10736.5	−1.52709	−0.763545	+	0.645754i	$0.776543\pi$
$368$	−20599.8	−2.91805
$369$	−7088.23	−0.999996
$370$	−3814.19	−0.535919
$371$	−7548.11	−1.05628
$372$	2994.23	0.417321
$373$	−2293.02	−0.318306	−0.159153	−	0.987254i	$-0.550876\pi$
$373$	−2293.02	−0.318306	−0.159153	+	0.987254i	$0.550876\pi$
$374$	1533.40	0.212006
$375$	−1956.92	−0.269479
$376$	−28530.0	−3.91309
$377$	−2837.54	−0.387641
$378$	23087.9	3.14158
$379$	427.679	0.0579641	0.0289820	−	0.999580i	$-0.490773\pi$
$379$	427.679	0.0579641	0.0289820	+	0.999580i	$0.490773\pi$
$380$	−1016.71	−0.137252
$381$	−62.6252	−0.00842097
$382$	−12719.4	−1.70362
$383$	2449.51	0.326800	0.163400	−	0.986560i	$-0.447754\pi$
$383$	2449.51	0.326800	0.163400	+	0.986560i	$0.447754\pi$
$384$	8436.21	1.12112
$385$	4923.82	0.651795
$386$	25949.5	3.42174
$387$	0	0
$388$	13272.7	1.73664
$389$	6014.07	0.783871	0.391935	−	0.919993i	$-0.371806\pi$
$389$	6014.07	0.783871	0.391935	+	0.919993i	$0.371806\pi$
$390$	999.817	0.129815
$391$	633.587	0.0819485
$392$	66154.5	8.52375
$393$	4370.75	0.561005
$394$	−10717.2	−1.37037
$395$	536.627	0.0683560
$396$	18672.1	2.36947
$397$	−6215.54	−0.785766	−0.392883	−	0.919588i	$-0.628522\pi$
$397$	−6215.54	−0.785766	−0.392883	+	0.919588i	$0.628522\pi$
$398$	13518.4	1.70256
$399$	1320.85	0.165727
$400$	−24801.1	−3.10014
$401$	−10720.5	−1.33505	−0.667525	−	0.744587i	$-0.732646\pi$
$401$	−10720.5	−1.33505	−0.667525	+	0.744587i	$0.732646\pi$
$402$	−1926.79	−0.239054
$403$	1269.03	0.156861
$404$	−2386.97	−0.293951
$405$	833.253	0.102234
$406$	24141.0	2.95098
$407$	9241.65	1.12553
$408$	−1198.76	−0.145460
$409$	7818.02	0.945174	0.472587	−	0.881284i	$-0.343320\pi$
$409$	7818.02	0.945174	0.472587	+	0.881284i	$0.343320\pi$
$410$	6022.37	0.725424
$411$	1376.96	0.165257
$412$	−34884.2	−4.17142
$413$	15503.1	1.84711
$414$	10623.1	1.26110
$415$	−3921.75	−0.463882
$416$	13567.8	1.59908
$417$	5181.62	0.608501
$418$	3391.94	0.396903
$419$	−11145.2	−1.29947	−0.649734	−	0.760162i	$-0.725120\pi$
$419$	−11145.2	−1.29947	−0.649734	+	0.760162i	$0.725120\pi$
$420$	−6177.72	−0.717719
$421$	2337.34	0.270582	0.135291	−	0.990806i	$-0.456803\pi$
$421$	2337.34	0.270582	0.135291	+	0.990806i	$0.456803\pi$
$422$	−28746.5	−3.31602
$423$	8249.01	0.948182
$424$	15153.4	1.73565
$425$	762.804	0.0870622
$426$	−8603.90	−0.978545
$427$	−24698.7	−2.79919
$428$	18371.1	2.07477
$429$	−2422.53	−0.272636
$430$	0	0
$431$	−14704.4	−1.64335	−0.821675	−	0.569956i	$-0.806960\pi$
$431$	−14704.4	−1.64335	−0.821675	+	0.569956i	$0.806960\pi$
$432$	−25988.0	−2.89432
$433$	10162.1	1.12785	0.563927	−	0.825824i	$-0.309290\pi$
$433$	10162.1	1.12785	0.563927	+	0.825824i	$0.309290\pi$
$434$	−10796.6	−1.19413
$435$	−1024.79	−0.112954
$436$	3132.88	0.344123
$437$	1401.52	0.153418
$438$	10021.4	1.09324
$439$	1142.15	0.124173	0.0620865	−	0.998071i	$-0.480225\pi$
$439$	1142.15	0.124173	0.0620865	+	0.998071i	$0.480225\pi$
$440$	−9884.95	−1.07101
$441$	−19127.6	−2.06539
$442$	−815.400	−0.0877480
$443$	4576.56	0.490832	0.245416	−	0.969418i	$-0.421075\pi$
$443$	4576.56	0.490832	0.245416	+	0.969418i	$0.421075\pi$
$444$	−11595.1	−1.23937
$445$	−1251.49	−0.133317
$446$	32531.1	3.45380
$447$	−1462.37	−0.154738
$448$	−53690.2	−5.66210
$449$	−4519.77	−0.475058	−0.237529	−	0.971380i	$-0.576337\pi$
$449$	−4519.77	−0.475058	−0.237529	+	0.971380i	$0.576337\pi$
$450$	12789.6	1.33979
$451$	−14592.0	−1.52353
$452$	−31521.9	−3.28023
$453$	734.320	0.0761619
$454$	7160.82	0.740251
$455$	−2618.29	−0.269774
$456$	−2651.71	−0.272319
$457$	−12268.8	−1.25582	−0.627911	−	0.778285i	$-0.716090\pi$
$457$	−12268.8	−1.25582	−0.627911	+	0.778285i	$0.716090\pi$
$458$	−14173.5	−1.44603
$459$	799.308	0.0812821
$460$	−6555.02	−0.664412
$461$	−17870.5	−1.80545	−0.902725	−	0.430219i	$-0.858436\pi$
$461$	−17870.5	−1.80545	−0.902725	+	0.430219i	$0.858436\pi$
$462$	20610.2	2.07548
$463$	12183.2	1.22289	0.611447	−	0.791285i	$-0.290588\pi$
$463$	12183.2	1.22289	0.611447	+	0.791285i	$0.290588\pi$
$464$	−27173.3	−2.71872
$465$	458.317	0.0457074
$466$	−27765.8	−2.76014
$467$	−2853.02	−0.282703	−0.141351	−	0.989959i	$-0.545145\pi$
$467$	−2853.02	−0.282703	−0.141351	+	0.989959i	$0.545145\pi$
$468$	−9929.08	−0.980709
$469$	5045.81	0.496789
$470$	−7008.61	−0.687836
$471$	2816.66	0.275551
$472$	−31123.6	−3.03513
$473$	0	0
$474$	2246.22	0.217663
$475$	1687.35	0.162992
$476$	5038.24	0.485141
$477$	−4381.38	−0.420565
$478$	−16676.6	−1.59575
$479$	−9303.99	−0.887495	−0.443748	−	0.896152i	$-0.646351\pi$
$479$	−9303.99	−0.887495	−0.443748	+	0.896152i	$0.646351\pi$
$480$	4900.07	0.465951
$481$	−4914.34	−0.465851
$482$	12701.1	1.20024
$483$	8515.93	0.802253
$484$	10188.2	0.956817
$485$	2031.61	0.190207
$486$	20991.9	1.95929
$487$	−15240.7	−1.41811	−0.709057	−	0.705151i	$-0.750879\pi$
$487$	−15240.7	−1.41811	−0.709057	+	0.705151i	$0.750879\pi$
$488$	49584.5	4.59956
$489$	−4910.99	−0.454157
$490$	16251.4	1.49829
$491$	13785.4	1.26706	0.633531	−	0.773717i	$-0.281605\pi$
$491$	13785.4	1.26706	0.633531	+	0.773717i	$0.281605\pi$
$492$	18308.0	1.67762
$493$	835.764	0.0763508
$494$	−1803.70	−0.164276
$495$	2858.08	0.259518
$496$	12152.7	1.10015
$497$	22531.6	2.03356
$498$	−16415.7	−1.47712
$499$	19041.0	1.70820	0.854100	−	0.520110i	$-0.174109\pi$
$499$	19041.0	1.70820	0.854100	+	0.520110i	$0.174109\pi$
$500$	−16511.7	−1.47685
$501$	5392.72	0.480896
$502$	−14247.5	−1.26673
$503$	1851.16	0.164094	0.0820470	−	0.996628i	$-0.473854\pi$
$503$	1851.16	0.164094	0.0820470	+	0.996628i	$0.473854\pi$
$504$	52634.8	4.65187
$505$	−365.365	−0.0321951
$506$	21868.9	1.92133
$507$	−4238.47	−0.371277
$508$	−528.406	−0.0461500
$509$	4035.03	0.351374	0.175687	−	0.984446i	$-0.443785\pi$
$509$	4035.03	0.351374	0.175687	+	0.984446i	$0.443785\pi$
$510$	−294.485	−0.0255686
$511$	−26243.6	−2.27191
$512$	5980.24	0.516194
$513$	1768.10	0.152171
$514$	13352.0	1.14578
$515$	−5339.62	−0.456877
$516$	0	0
$517$	16981.6	1.44459
$518$	41809.8	3.54637
$519$	−1041.95	−0.0881245
$520$	5256.42	0.443287
$521$	−10876.5	−0.914602	−0.457301	−	0.889312i	$-0.651184\pi$
$521$	−10876.5	−0.914602	−0.457301	+	0.889312i	$0.651184\pi$
$522$	14012.9	1.17496
$523$	−7571.06	−0.633001	−0.316500	−	0.948592i	$-0.602508\pi$
$523$	−7571.06	−0.633001	−0.316500	+	0.948592i	$0.602508\pi$
$524$	36878.6	3.07452
$525$	10252.7	0.852315
$526$	−6993.64	−0.579728
$527$	−373.780	−0.0308958
$528$	−23199.0	−1.91213
$529$	−3130.97	−0.257333
$530$	3722.55	0.305089
$531$	8998.92	0.735442
$532$	11144.8	0.908247
$533$	7759.44	0.630579
$534$	−5238.48	−0.424515
$535$	2812.00	0.227240
$536$	−10129.9	−0.816312
$537$	1004.21	0.0806978
$538$	−18080.5	−1.44890
$539$	−39376.5	−3.14669
$540$	−8269.56	−0.659010
$541$	9311.57	0.739992	0.369996	−	0.929033i	$-0.379359\pi$
$541$	9311.57	0.739992	0.369996	+	0.929033i	$0.379359\pi$
$542$	8283.52	0.656472
$543$	2133.34	0.168601
$544$	−3996.25	−0.314959
$545$	479.539	0.0376903
$546$	−10959.7	−0.859029
$547$	19005.3	1.48557	0.742787	−	0.669528i	$-0.233504\pi$
$547$	19005.3	1.48557	0.742787	+	0.669528i	$0.233504\pi$
$548$	11618.2	0.905667
$549$	−14336.6	−1.11452
$550$	26329.0	2.04122
$551$	1848.74	0.142939
$552$	−17096.4	−1.31824
$553$	−5882.32	−0.452336
$554$	35083.9	2.69056
$555$	−1774.83	−0.135743
$556$	43720.3	3.33481
$557$	20799.6	1.58224	0.791122	−	0.611659i	$-0.209498\pi$
$557$	20799.6	1.58224	0.791122	+	0.611659i	$0.209498\pi$
$558$	−6267.00	−0.475454
$559$	0	0
$560$	−25073.7	−1.89206
$561$	713.527	0.0536990
$562$	−15473.6	−1.16141
$563$	16633.6	1.24516	0.622580	−	0.782556i	$-0.286085\pi$
$563$	16633.6	1.24516	0.622580	+	0.782556i	$0.286085\pi$
$564$	−21306.2	−1.59070
$565$	−4824.95	−0.359269
$566$	32107.8	2.38444
$567$	−9133.84	−0.676517
$568$	−45233.9	−3.34150
$569$	−15215.4	−1.12102	−0.560511	−	0.828147i	$-0.689395\pi$
$569$	−15215.4	−1.12102	−0.560511	+	0.828147i	$0.689395\pi$
$570$	−651.412	−0.0478678
$571$	4026.41	0.295096	0.147548	−	0.989055i	$-0.452862\pi$
$571$	4026.41	0.295096	0.147548	+	0.989055i	$0.452862\pi$
$572$	−20440.3	−1.49414
$573$	−5918.66	−0.431510
$574$	−66015.2	−4.80039
$575$	10878.9	0.789011
$576$	−31165.0	−2.25442
$577$	15767.5	1.13762	0.568811	−	0.822468i	$-0.307404\pi$
$577$	15767.5	1.13762	0.568811	+	0.822468i	$0.307404\pi$
$578$	−26319.7	−1.89404
$579$	12074.9	0.866693
$580$	−8646.73	−0.619028
$581$	42988.9	3.06967
$582$	8503.91	0.605668
$583$	−9019.62	−0.640746
$584$	52686.0	3.73316
$585$	−1519.81	−0.107413
$586$	40352.1	2.84459
$587$	19862.5	1.39661	0.698307	−	0.715798i	$-0.253937\pi$
$587$	19862.5	1.39661	0.698307	+	0.715798i	$0.253937\pi$
$588$	49404.2	3.46496
$589$	−826.816	−0.0578410
$590$	−7645.75	−0.533509
$591$	−4986.97	−0.347100
$592$	−47061.4	−3.26725
$593$	−23932.8	−1.65734	−0.828670	−	0.559738i	$-0.810902\pi$
$593$	−23932.8	−1.65734	−0.828670	+	0.559738i	$0.810902\pi$
$594$	27589.0	1.90571
$595$	771.187	0.0531354
$596$	−12338.9	−0.848020
$597$	6290.44	0.431241
$598$	−11629.0	−0.795226
$599$	−14604.5	−0.996202	−0.498101	−	0.867119i	$-0.665969\pi$
$599$	−14604.5	−0.996202	−0.498101	+	0.867119i	$0.665969\pi$
$600$	−20583.1	−1.40051
$601$	52.6820	0.00357561	0.00178781	−	0.999998i	$-0.499431\pi$
$601$	52.6820	0.00357561	0.00178781	+	0.999998i	$0.499431\pi$
$602$	0	0
$603$	2928.89	0.197801
$604$	6195.89	0.417396
$605$	1559.47	0.104796
$606$	−1529.35	−0.102518
$607$	9852.75	0.658832	0.329416	−	0.944185i	$-0.393148\pi$
$607$	9852.75	0.658832	0.329416	+	0.944185i	$0.393148\pi$
$608$	−8839.86	−0.589644
$609$	11233.4	0.747453
$610$	12180.8	0.808503
$611$	−9030.15	−0.597906
$612$	2924.50	0.193163
$613$	−12503.9	−0.823861	−0.411930	−	0.911215i	$-0.635145\pi$
$613$	−12503.9	−0.823861	−0.411930	+	0.911215i	$0.635145\pi$
$614$	−7724.57	−0.507717
$615$	2802.35	0.183743
$616$	108355.	7.08728
$617$	2356.04	0.153729	0.0768644	−	0.997042i	$-0.475509\pi$
$617$	2356.04	0.153729	0.0768644	+	0.997042i	$0.475509\pi$
$618$	−22350.6	−1.45481
$619$	−5749.87	−0.373355	−0.186678	−	0.982421i	$-0.559772\pi$
$619$	−5749.87	−0.373355	−0.186678	+	0.982421i	$0.559772\pi$
$620$	3867.09	0.250493
$621$	11399.5	0.736629
$622$	−33346.0	−2.14960
$623$	13718.4	0.882206
$624$	12336.3	0.791420
$625$	11778.2	0.753806
$626$	−1129.33	−0.0721038
$627$	1578.35	0.100532
$628$	23765.8	1.51012
$629$	1447.46	0.0917553
$630$	12930.1	0.817697
$631$	−23912.8	−1.50864	−0.754322	−	0.656505i	$-0.772034\pi$
$631$	−23912.8	−1.50864	−0.754322	+	0.656505i	$0.772034\pi$
$632$	11809.2	0.743268
$633$	−13376.4	−0.839914
$634$	−2122.04	−0.132929
$635$	−80.8814	−0.00505461
$636$	11316.6	0.705552
$637$	20938.8	1.30240
$638$	28847.3	1.79009
$639$	13078.7	0.809680
$640$	10895.5	0.672940
$641$	4628.89	0.285226	0.142613	−	0.989778i	$-0.454449\pi$
$641$	4628.89	0.285226	0.142613	+	0.989778i	$0.454449\pi$
$642$	11770.5	0.723591
$643$	−30231.9	−1.85417	−0.927085	−	0.374852i	$-0.877693\pi$
$643$	−30231.9	−1.85417	−0.927085	+	0.374852i	$0.877693\pi$
$644$	71853.9	4.39665
$645$	0	0
$646$	531.259	0.0323562
$647$	−6207.36	−0.377181	−0.188591	−	0.982056i	$-0.560392\pi$
$647$	−6207.36	−0.377181	−0.188591	+	0.982056i	$0.560392\pi$
$648$	18336.9	1.11164
$649$	18525.4	1.12047
$650$	−14000.7	−0.844850
$651$	−5023.91	−0.302462
$652$	−41436.9	−2.48895
$653$	−2288.32	−0.137135	−0.0685674	−	0.997646i	$-0.521843\pi$
$653$	−2288.32	−0.137135	−0.0685674	+	0.997646i	$0.521843\pi$
$654$	2007.26	0.120015
$655$	5644.89	0.336739
$656$	74307.2	4.42257
$657$	−15233.4	−0.904581
$658$	76826.0	4.55165
$659$	2633.73	0.155684	0.0778419	−	0.996966i	$-0.475197\pi$
$659$	2633.73	0.155684	0.0778419	+	0.996966i	$0.475197\pi$
$660$	−7382.08	−0.435374
$661$	−26447.4	−1.55625	−0.778127	−	0.628107i	$-0.783830\pi$
$661$	−26447.4	−1.55625	−0.778127	+	0.628107i	$0.783830\pi$
$662$	−10001.9	−0.587212
$663$	−379.425	−0.0222257
$664$	−86303.5	−5.04401
$665$	1705.90	0.0994764
$666$	24268.9	1.41202
$667$	11919.4	0.691938
$668$	45501.5	2.63549
$669$	15137.5	0.874813
$670$	−2488.48	−0.143490
$671$	−29513.7	−1.69801
$672$	−53712.9	−3.08336
$673$	18756.0	1.07428	0.537141	−	0.843493i	$-0.319504\pi$
$673$	18756.0	1.07428	0.537141	+	0.843493i	$0.319504\pi$
$674$	−15655.6	−0.894706
$675$	13724.4	0.782596
$676$	−35762.5	−2.03473
$677$	18144.7	1.03007	0.515034	−	0.857170i	$-0.327779\pi$
$677$	18144.7	1.03007	0.515034	+	0.857170i	$0.327779\pi$
$678$	−20196.3	−1.14401
$679$	−22269.8	−1.25867
$680$	−1548.22	−0.0873109
$681$	3332.10	0.187498
$682$	−12901.4	−0.724370
$683$	15347.3	0.859807	0.429904	−	0.902875i	$-0.358548\pi$
$683$	15347.3	0.859807	0.429904	+	0.902875i	$0.358548\pi$
$684$	6469.11	0.361626
$685$	1778.36	0.0991938
$686$	−112106.	−6.23938
$687$	−6595.25	−0.366266
$688$	0	0
$689$	4796.27	0.265201
$690$	−4199.86	−0.231719
$691$	7277.80	0.400667	0.200333	−	0.979728i	$-0.435797\pi$
$691$	7277.80	0.400667	0.200333	+	0.979728i	$0.435797\pi$
$692$	−8791.56	−0.482955
$693$	−31329.3	−1.71732
$694$	−53032.3	−2.90069
$695$	6692.13	0.365248
$696$	−22551.9	−1.22820
$697$	−2285.46	−0.124201
$698$	−20695.3	−1.12225
$699$	−12920.1	−0.699116
$700$	86508.2	4.67101
$701$	−1386.84	−0.0747223	−0.0373612	−	0.999302i	$-0.511895\pi$
$701$	−1386.84	−0.0747223	−0.0373612	+	0.999302i	$0.511895\pi$
$702$	−14670.7	−0.788760
$703$	3201.84	0.171778
$704$	−64157.2	−3.43468
$705$	−3261.27	−0.174222
$706$	42049.8	2.24160
$707$	4005.01	0.213047
$708$	−23243.1	−1.23380
$709$	26596.1	1.40880	0.704399	−	0.709804i	$-0.251217\pi$
$709$	26596.1	1.40880	0.704399	+	0.709804i	$0.251217\pi$
$710$	−11112.1	−0.587364
$711$	−3414.46	−0.180101
$712$	−27540.7	−1.44962
$713$	−5330.74	−0.279997
$714$	3228.04	0.169197
$715$	−3128.73	−0.163647
$716$	8473.08	0.442254
$717$	−7759.99	−0.404187
$718$	14513.6	0.754379
$719$	22649.9	1.17482	0.587412	−	0.809288i	$-0.300147\pi$
$719$	22649.9	1.17482	0.587412	+	0.809288i	$0.300147\pi$
$720$	−14554.3	−0.753341
$721$	58531.1	3.02332
$722$	−35904.8	−1.85075
$723$	5910.11	0.304010
$724$	18000.3	0.923998
$725$	14350.4	0.735116
$726$	6527.66	0.333697
$727$	−35825.5	−1.82764	−0.913821	−	0.406117i	$-0.866883\pi$
$727$	−35825.5	−1.82764	−0.913821	+	0.406117i	$0.866883\pi$
$728$	−57619.0	−2.93338
$729$	2843.23	0.144451
$730$	12942.7	0.656208
$731$	0	0
$732$	37029.7	1.86975
$733$	−34195.3	−1.72310	−0.861549	−	0.507674i	$-0.830505\pi$
$733$	−34195.3	−1.72310	−0.861549	+	0.507674i	$0.830505\pi$
$734$	−58042.1	−2.91876
$735$	7562.14	0.379502
$736$	−56993.4	−2.85435
$737$	6029.50	0.301356
$738$	−38319.2	−1.91131
$739$	28264.3	1.40693	0.703464	−	0.710731i	$-0.251636\pi$
$739$	28264.3	1.40693	0.703464	+	0.710731i	$0.251636\pi$
$740$	−14975.3	−0.743922
$741$	−839.303	−0.0416094
$742$	−40805.3	−2.01888
$743$	12755.5	0.629815	0.314908	−	0.949122i	$-0.398026\pi$
$743$	12755.5	0.629815	0.314908	+	0.949122i	$0.398026\pi$
$744$	10085.9	0.496998
$745$	−1888.67	−0.0928799
$746$	−12396.2	−0.608385
$747$	24953.3	1.22222
$748$	6020.45	0.294291
$749$	−30824.2	−1.50373
$750$	−10579.2	−0.515062
$751$	22857.6	1.11064	0.555318	−	0.831638i	$-0.312597\pi$
$751$	22857.6	1.11064	0.555318	+	0.831638i	$0.312597\pi$
$752$	−86475.9	−4.19342
$753$	−6629.71	−0.320850
$754$	−15339.8	−0.740907
$755$	948.385	0.0457156
$756$	90648.1	4.36090
$757$	−6240.07	−0.299603	−0.149801	−	0.988716i	$-0.547863\pi$
$757$	−6240.07	−0.299603	−0.149801	+	0.988716i	$0.547863\pi$
$758$	2312.05	0.110788
$759$	10176.1	0.486653
$760$	−3424.72	−0.163457
$761$	13726.9	0.653875	0.326938	−	0.945046i	$-0.393983\pi$
$761$	13726.9	0.653875	0.326938	+	0.945046i	$0.393983\pi$
$762$	−338.554	−0.0160952
$763$	−5256.55	−0.249410
$764$	−49939.2	−2.36484
$765$	447.644	0.0211563
$766$	13242.2	0.624619
$767$	−9851.06	−0.463756
$768$	15266.9	0.717313
$769$	5526.73	0.259167	0.129583	−	0.991569i	$-0.458636\pi$
$769$	5526.73	0.259167	0.129583	+	0.991569i	$0.458636\pi$
$770$	26618.3	1.24579
$771$	6213.02	0.290216
$772$	101883.	4.74980
$773$	25950.2	1.20746	0.603728	−	0.797191i	$-0.293681\pi$
$773$	25950.2	1.20746	0.603728	+	0.797191i	$0.293681\pi$
$774$	0	0
$775$	−6417.93	−0.297469
$776$	44708.3	2.06821
$777$	19455.1	0.898259
$778$	32512.3	1.49823
$779$	−5055.52	−0.232520
$780$	3925.49	0.180199
$781$	26924.2	1.23358
$782$	3425.19	0.156630
$783$	15037.1	0.686311
$784$	200518.	9.13438
$785$	3637.75	0.165397
$786$	23628.4	1.07226
$787$	−29492.7	−1.33583	−0.667917	−	0.744235i	$-0.732814\pi$
$787$	−29492.7	−1.33583	−0.667917	+	0.744235i	$0.732814\pi$
$788$	−42078.0	−1.90224
$789$	−3254.30	−0.146839
$790$	2901.02	0.130650
$791$	52889.5	2.37741
$792$	62896.1	2.82186
$793$	15694.2	0.702797
$794$	−33601.4	−1.50185
$795$	1732.19	0.0772761
$796$	53076.2	2.36336
$797$	−34997.7	−1.55543	−0.777717	−	0.628614i	$-0.783622\pi$
$797$	−34997.7	−1.55543	−0.777717	+	0.628614i	$0.783622\pi$
$798$	7140.56	0.316758
$799$	2659.73	0.117765
$800$	−68617.0	−3.03247
$801$	7962.96	0.351258
$802$	−57955.3	−2.55171
$803$	−31359.8	−1.37816
$804$	−7564.98	−0.331836
$805$	10998.4	0.481546
$806$	6860.45	0.299813
$807$	−8413.29	−0.366991
$808$	−8040.37	−0.350073
$809$	32571.8	1.41553	0.707766	−	0.706447i	$-0.249703\pi$
$809$	32571.8	1.41553	0.707766	+	0.706447i	$0.249703\pi$
$810$	4504.60	0.195402
$811$	28857.9	1.24949	0.624747	−	0.780828i	$-0.285202\pi$
$811$	28857.9	1.24949	0.624747	+	0.780828i	$0.285202\pi$
$812$	94782.5	4.09632
$813$	3854.52	0.166278
$814$	49960.7	2.15126
$815$	−6342.62	−0.272604
$816$	−3633.51	−0.155880
$817$	0	0
$818$	42264.5	1.80653
$819$	16659.7	0.710789
$820$	23645.1	1.00698
$821$	−12710.1	−0.540300	−0.270150	−	0.962818i	$-0.587073\pi$
$821$	−12710.1	−0.540300	−0.270150	+	0.962818i	$0.587073\pi$
$822$	7443.89	0.315858
$823$	−8447.81	−0.357803	−0.178902	−	0.983867i	$-0.557254\pi$
$823$	−8447.81	−0.357803	−0.178902	+	0.983867i	$0.557254\pi$
$824$	−117506.	−4.96784
$825$	12251.5	0.517022
$826$	83810.1	3.53042
$827$	−8494.53	−0.357175	−0.178588	−	0.983924i	$-0.557153\pi$
$827$	−8494.53	−0.357175	−0.178588	+	0.983924i	$0.557153\pi$
$828$	41708.4	1.75056
$829$	−28640.7	−1.19992	−0.599959	−	0.800031i	$-0.704816\pi$
$829$	−28640.7	−1.19992	−0.599959	+	0.800031i	$0.704816\pi$
$830$	−21201.1	−0.886628
$831$	16325.4	0.681493
$832$	34116.2	1.42159
$833$	−6167.30	−0.256524
$834$	28012.0	1.16304
$835$	6964.77	0.288654
$836$	13317.5	0.550950
$837$	−6725.05	−0.277720
$838$	−60251.2	−2.48370
$839$	−20471.9	−0.842393	−0.421196	−	0.906969i	$-0.638390\pi$
$839$	−20471.9	−0.842393	−0.421196	+	0.906969i	$0.638390\pi$
$840$	−20809.3	−0.854750
$841$	−8666.07	−0.355327
$842$	12635.7	0.517169
$843$	−7200.21	−0.294174
$844$	−112865.	−4.60304
$845$	−5474.05	−0.222856
$846$	44594.5	1.81228
$847$	−17094.4	−0.693472
$848$	45930.8	1.85999
$849$	14940.5	0.603954
$850$	4123.75	0.166404
$851$	20643.3	0.831543
$852$	−33780.7	−1.35834
$853$	−32548.6	−1.30650	−0.653249	−	0.757143i	$-0.726595\pi$
$853$	−32548.6	−1.30650	−0.653249	+	0.757143i	$0.726595\pi$
$854$	−133522.	−5.35015
$855$	990.205	0.0396074
$856$	61882.0	2.47089
$857$	−19607.8	−0.781553	−0.390776	−	0.920486i	$-0.627793\pi$
$857$	−19607.8	−0.781553	−0.390776	+	0.920486i	$0.627793\pi$
$858$	−13096.3	−0.521094
$859$	−36871.0	−1.46452	−0.732259	−	0.681026i	$-0.761534\pi$
$859$	−36871.0	−1.46452	−0.732259	+	0.681026i	$0.761534\pi$
$860$	0	0
$861$	−30718.4	−1.21589
$862$	−79492.3	−3.14097
$863$	21302.4	0.840259	0.420130	−	0.907464i	$-0.361985\pi$
$863$	21302.4	0.840259	0.420130	+	0.907464i	$0.361985\pi$
$864$	−71900.6	−2.83114
$865$	−1345.70	−0.0528960
$866$	54936.9	2.15569
$867$	−12247.2	−0.479741
$868$	−42389.7	−1.65760
$869$	−7029.09	−0.274391
$870$	−5540.04	−0.215891
$871$	−3206.24	−0.124730
$872$	10552.9	0.409825
$873$	−12926.7	−0.501149
$874$	7576.66	0.293232
$875$	27704.3	1.07037
$876$	39345.9	1.51755
$877$	−1799.88	−0.0693016	−0.0346508	−	0.999399i	$-0.511032\pi$
$877$	−1799.88	−0.0693016	−0.0346508	+	0.999399i	$0.511032\pi$
$878$	6174.52	0.237335
$879$	18776.8	0.720506
$880$	−29961.8	−1.14774
$881$	−7632.90	−0.291894	−0.145947	−	0.989292i	$-0.546623\pi$
$881$	−7632.90	−0.291894	−0.145947	+	0.989292i	$0.546623\pi$
$882$	−103404.	−3.94763
$883$	−7483.72	−0.285218	−0.142609	−	0.989779i	$-0.545549\pi$
$883$	−7483.72	−0.285218	−0.142609	+	0.989779i	$0.545549\pi$
$884$	−3201.43	−0.121805
$885$	−3557.75	−0.135133
$886$	24741.0	0.938139
$887$	16767.7	0.634728	0.317364	−	0.948304i	$-0.397202\pi$
$887$	16767.7	0.634728	0.317364	+	0.948304i	$0.397202\pi$
$888$	−39057.6	−1.47600
$889$	886.594	0.0334482
$890$	−6765.57	−0.254812
$891$	−10914.5	−0.410381
$892$	127724.	4.79430
$893$	5883.42	0.220472
$894$	−7905.62	−0.295753
$895$	1296.95	0.0484382
$896$	−119433.	−4.45308
$897$	−5411.25	−0.201423
$898$	−24434.0	−0.907989
$899$	−7031.78	−0.260871
$900$	50214.6	1.85980
$901$	−1412.69	−0.0522347
$902$	−78885.0	−2.91195
$903$	0	0
$904$	−106180.	−3.90651
$905$	2755.24	0.101201
$906$	3969.76	0.145570
$907$	−42555.8	−1.55793	−0.778965	−	0.627068i	$-0.784255\pi$
$907$	−42555.8	−1.55793	−0.778965	+	0.627068i	$0.784255\pi$
$908$	28114.9	1.02756
$909$	2324.75	0.0848263
$910$	−14154.6	−0.515625
$911$	−24280.3	−0.883031	−0.441516	−	0.897254i	$-0.645559\pi$
$911$	−24280.3	−0.883031	−0.441516	+	0.897254i	$0.645559\pi$
$912$	−8037.46	−0.291828
$913$	51369.6	1.86209
$914$	−66325.6	−2.40028
$915$	5668.02	0.204786
$916$	−55648.0	−2.00727
$917$	−61877.3	−2.22832
$918$	4321.09	0.155356
$919$	11725.6	0.420883	0.210441	−	0.977606i	$-0.432510\pi$
$919$	11725.6	0.420883	0.210441	+	0.977606i	$0.432510\pi$
$920$	−22080.2	−0.791265
$921$	−3594.42	−0.128600
$922$	−96608.6	−3.45080
$923$	−14317.2	−0.510570
$924$	80919.8	2.88102
$925$	24853.4	0.883433
$926$	65862.6	2.33734
$927$	33975.0	1.20376
$928$	−75180.0	−2.65938
$929$	2787.61	0.0984484	0.0492242	−	0.998788i	$-0.484325\pi$
$929$	2787.61	0.0984484	0.0492242	+	0.998788i	$0.484325\pi$
$930$	2477.68	0.0873615
$931$	−13642.3	−0.480246
$932$	−109014.	−3.83141
$933$	−15516.7	−0.544473
$934$	−15423.5	−0.540336
$935$	921.531	0.0322324
$936$	−33445.6	−1.16795
$937$	9008.26	0.314074	0.157037	−	0.987593i	$-0.449806\pi$
$937$	9008.26	0.314074	0.157037	+	0.987593i	$0.449806\pi$
$938$	27277.8	0.949523
$939$	−525.502	−0.0182632
$940$	−27517.3	−0.954802
$941$	−22821.0	−0.790586	−0.395293	−	0.918555i	$-0.629357\pi$
$941$	−22821.0	−0.790586	−0.395293	+	0.918555i	$0.629357\pi$
$942$	15226.9	0.526667
$943$	−32594.5	−1.12558
$944$	−94337.2	−3.25256
$945$	13875.2	0.477630
$946$	0	0
$947$	−22989.4	−0.788864	−0.394432	−	0.918925i	$-0.629059\pi$
$947$	−22989.4	−0.788864	−0.394432	+	0.918925i	$0.629059\pi$
$948$	8819.12	0.302143
$949$	16675.9	0.570413
$950$	9121.89	0.311530
$951$	−987.436	−0.0336696
$952$	16971.0	0.577767
$953$	−40326.5	−1.37073	−0.685364	−	0.728201i	$-0.740357\pi$
$953$	−40326.5	−1.37073	−0.685364	+	0.728201i	$0.740357\pi$
$954$	−23685.9	−0.803836
$955$	−7644.03	−0.259011
$956$	−65475.6	−2.21510
$957$	13423.3	0.453411
$958$	−50297.7	−1.69629
$959$	−19493.8	−0.656400
$960$	12321.2	0.414234
$961$	−26646.2	−0.894437
$962$	−26567.1	−0.890392
$963$	−17892.3	−0.598722
$964$	49867.0	1.66609
$965$	15594.9	0.520226
$966$	46037.4	1.53336
$967$	17638.8	0.586581	0.293291	−	0.956023i	$-0.405250\pi$
$967$	17638.8	0.586581	0.293291	+	0.956023i	$0.405250\pi$
$968$	34318.3	1.13950
$969$	247.207	0.00819550
$970$	10982.9	0.363547
$971$	−27474.1	−0.908019	−0.454010	−	0.890997i	$-0.650007\pi$
$971$	−27474.1	−0.908019	−0.454010	+	0.890997i	$0.650007\pi$
$972$	82418.7	2.71973
$973$	−73356.9	−2.41697
$974$	−82391.7	−2.71047
$975$	−6514.86	−0.213992
$976$	150293.	4.92907
$977$	−35587.3	−1.16534	−0.582671	−	0.812708i	$-0.697992\pi$
$977$	−35587.3	−1.16534	−0.582671	+	0.812708i	$0.697992\pi$
$978$	−26549.0	−0.868040
$979$	16392.8	0.535153
$980$	63806.2	2.07981
$981$	−3051.22	−0.0993047
$982$	74524.5	2.42176
$983$	16027.0	0.520023	0.260012	−	0.965605i	$-0.416274\pi$
$983$	16027.0	0.520023	0.260012	+	0.965605i	$0.416274\pi$
$984$	61669.6	1.99792
$985$	−6440.74	−0.208344
$986$	4518.17	0.145931
$987$	35748.9	1.15289
$988$	−7081.69	−0.228035
$989$	0	0
$990$	15450.9	0.496022
$991$	−8618.18	−0.276252	−0.138126	−	0.990415i	$-0.544108\pi$
$991$	−8618.18	−0.276252	−0.138126	+	0.990415i	$0.544108\pi$
$992$	33622.8	1.07613
$993$	−4654.11	−0.148735
$994$	121807.	3.88679
$995$	8124.20	0.258849
$996$	−64451.4	−2.05042
$997$	30698.8	0.975166	0.487583	−	0.873077i	$-0.337879\pi$
$997$	30698.8	0.975166	0.487583	+	0.873077i	$0.337879\pi$
$998$	102936.	3.26492
$999$	26042.8	0.824781

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.j.1.49	yes	50
43.42	odd	2		1849.4.a.i.1.2	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.2	✓	50	43.42	odd	2
1849.4.a.j.1.49	yes	50	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+5.40604 q^{2} +2.51556 q^{3} +21.2252 q^{4} +3.24888 q^{5} +13.5992 q^{6} -35.6131 q^{7} +71.4960 q^{8} -20.6720 q^{9} +O(q^{10})\)	\(q+5.40604 q^{2} +2.51556 q^{3} +21.2252 q^{4} +3.24888 q^{5} +13.5992 q^{6} -35.6131 q^{7} +71.4960 q^{8} -20.6720 q^{9} +17.5635 q^{10} -42.5559 q^{11} +53.3932 q^{12} +22.6295 q^{13} -192.525 q^{14} +8.17273 q^{15} +216.708 q^{16} -6.66526 q^{17} -111.753 q^{18} -14.7438 q^{19} +68.9581 q^{20} -89.5866 q^{21} -230.059 q^{22} -95.0580 q^{23} +179.852 q^{24} -114.445 q^{25} +122.336 q^{26} -119.922 q^{27} -755.895 q^{28} -125.391 q^{29} +44.1820 q^{30} +56.0788 q^{31} +599.564 q^{32} -107.052 q^{33} -36.0326 q^{34} -115.702 q^{35} -438.767 q^{36} -217.165 q^{37} -79.7056 q^{38} +56.9257 q^{39} +232.282 q^{40} +342.891 q^{41} -484.308 q^{42} -903.258 q^{44} -67.1607 q^{45} -513.887 q^{46} -399.043 q^{47} +545.141 q^{48} +925.290 q^{49} -618.693 q^{50} -16.7668 q^{51} +480.316 q^{52} +211.948 q^{53} -648.300 q^{54} -138.259 q^{55} -2546.19 q^{56} -37.0889 q^{57} -677.869 q^{58} -435.319 q^{59} +173.468 q^{60} +693.529 q^{61} +303.164 q^{62} +736.193 q^{63} +1507.60 q^{64} +73.5204 q^{65} -578.725 q^{66} -141.684 q^{67} -141.472 q^{68} -239.124 q^{69} -625.491 q^{70} -632.678 q^{71} -1477.96 q^{72} +736.909 q^{73} -1174.00 q^{74} -287.892 q^{75} -312.941 q^{76} +1515.55 q^{77} +307.743 q^{78} +165.173 q^{79} +704.058 q^{80} +256.474 q^{81} +1853.68 q^{82} -1207.11 q^{83} -1901.50 q^{84} -21.6546 q^{85} -315.428 q^{87} -3042.58 q^{88} -385.206 q^{89} -363.073 q^{90} -805.906 q^{91} -2017.63 q^{92} +141.069 q^{93} -2157.24 q^{94} -47.9008 q^{95} +1508.24 q^{96} +625.326 q^{97} +5002.15 q^{98} +879.715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 10 q^{2} + 2 q^{3} + 186 q^{4} - 8 q^{5} - 51 q^{6} + 6 q^{7} + 138 q^{8} + 360 q^{9}+O(q^{10}) \) 50 * q + 10 * q^2 + 2 * q^3 + 186 * q^4 - 8 * q^5 - 51 * q^6 + 6 * q^7 + 138 * q^8 + 360 * q^9	\( 50 q + 10 q^{2} + 2 q^{3} + 186 q^{4} - 8 q^{5} - 51 q^{6} + 6 q^{7} + 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} + 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} + 386 q^{18} - 12 q^{19} - 108 q^{20} - 408 q^{21} - 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} - 1493 q^{26} - 10 q^{27} + 242 q^{28} - 208 q^{29} + 48 q^{30} - 932 q^{31} + 1124 q^{32} - 254 q^{33} - 765 q^{34} - 1452 q^{35} + 747 q^{36} + 90 q^{37} - 1213 q^{38} + 1610 q^{39} - 1693 q^{40} - 1354 q^{41} + 16 q^{42} - 2704 q^{44} - 4508 q^{45} - 233 q^{46} - 3484 q^{47} + 376 q^{48} + 1324 q^{49} + 408 q^{50} - 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} + 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} - 1172 q^{61} + 1546 q^{62} + 3686 q^{63} + 606 q^{64} - 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} - 136 q^{69} + 1310 q^{70} - 162 q^{71} + 5814 q^{72} - 746 q^{73} - 4332 q^{74} - 236 q^{75} - 1338 q^{76} - 2024 q^{77} - 2782 q^{78} - 2656 q^{79} + 5713 q^{80} - 86 q^{81} + 4168 q^{82} - 3514 q^{83} - 4269 q^{84} + 7558 q^{85} - 10278 q^{87} - 11692 q^{88} - 2640 q^{89} - 8286 q^{90} + 5946 q^{91} - 4271 q^{92} + 2 q^{93} - 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} + 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q + 10 * q^2 + 2 * q^3 + 186 * q^4 - 8 * q^5 - 51 * q^6 + 6 * q^7 + 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 + 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 + 386 * q^18 - 12 * q^19 - 108 * q^20 - 408 * q^21 - 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 - 1493 * q^26 - 10 * q^27 + 242 * q^28 - 208 * q^29 + 48 * q^30 - 932 * q^31 + 1124 * q^32 - 254 * q^33 - 765 * q^34 - 1452 * q^35 + 747 * q^36 + 90 * q^37 - 1213 * q^38 + 1610 * q^39 - 1693 * q^40 - 1354 * q^41 + 16 * q^42 - 2704 * q^44 - 4508 * q^45 - 233 * q^46 - 3484 * q^47 + 376 * q^48 + 1324 * q^49 + 408 * q^50 - 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 + 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 - 1172 * q^61 + 1546 * q^62 + 3686 * q^63 + 606 * q^64 - 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 - 136 * q^69 + 1310 * q^70 - 162 * q^71 + 5814 * q^72 - 746 * q^73 - 4332 * q^74 - 236 * q^75 - 1338 * q^76 - 2024 * q^77 - 2782 * q^78 - 2656 * q^79 + 5713 * q^80 - 86 * q^81 + 4168 * q^82 - 3514 * q^83 - 4269 * q^84 + 7558 * q^85 - 10278 * q^87 - 11692 * q^88 - 2640 * q^89 - 8286 * q^90 + 5946 * q^91 - 4271 * q^92 + 2 * q^93 - 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 + 2826 * q^98 - 8174 * q^99

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